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TARGETS 4-6 Isosceles and Equilateral Triangles (Pg .283)
Use properties of isosceles triangles. Use properties of equilateral triangles. `
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Content Standards G-CO.10 Prove theorems about triangles.
G-CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. Mathematical Practices 2 Reason abstractly and quantitatively. 6 Attend to precision.
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Vocabulary, Key Concepts, and Theorems
Legs of and isosceles triangle Vertex angle Base angles Theorem 4.10 & 4.11 Corollary 4.3 & 4.4
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Concept
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A. Name two unmarked congruent angles.
Congruent Segments and Angles A. Name two unmarked congruent angles. BCA is opposite BA and A is opposite BC, so BCA A. ___ Answer: BCA and A Example 1
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B. Name two unmarked congruent segments.
Congruent Segments and Angles B. Name two unmarked congruent segments. ___ BC is opposite D and BD is opposite BCD, so BC BD. Answer: BC BD Example 1
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A. Which statement correctly names two congruent angles?
A. PJM PMJ B. JMK JKM C. KJP JKP D. PML PLK Example 1a
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B. Which statement correctly names two congruent segments?
A. JP PL B. PM PJ C. JK MK D. PM PK Example 1b
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Concept
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Subtract 60 from each side. Answer: mR = 60 Divide each side by 2.
Find Missing Measures A. Find mR. Since QP = QR, QP QR. By the Isosceles Triangle Theorem, base angles P and R are congruent, so mP = mR . Use the Triangle Sum Theorem to write and solve an equation to find mR. Triangle Sum Theorem mQ = 60, mP = mR Simplify. Subtract 60 from each side. Answer: mR = 60 Divide each side by 2. Example 2
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Find Missing Measures B. Find PR. Since all three angles measure 60, the triangle is equiangular. Because an equiangular triangle is also equilateral, QP = QR = PR. Since QP = 5, PR = 5 by substitution. Answer: PR = 5 cm Example 2
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A. Find mT. A. 30° B. 45° C. 60° D. 65° Example 2a
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B. Find TS. A. 1.5 B. 3.5 C. 4 D. 7 Example 2b
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ALGEBRA Find the value of each variable.
Find Missing Values ALGEBRA Find the value of each variable. Since E = F, DE FE by the Converse of the Isosceles Triangle Theorem. DF FE, so all of the sides of the triangle are congruent. The triangle is equilateral. Each angle of an equilateral triangle measures 60°. Example 3
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mDFE = 60 Definition of equilateral triangle 4x – 8 = 60 Substitution
Find Missing Values mDFE = 60 Definition of equilateral triangle 4x – 8 = 60 Substitution 4x = 68 Add 8 to each side. x = 17 Divide each side by 4. The triangle is equilateral, so all the sides are congruent, and the lengths of all of the sides are equal. DF = FE Definition of equilateral triangle 6y + 3 = 8y – 5 Substitution 3 = 2y – 5 Subtract 6y from each side. 8 = 2y Add 5 to each side. Example 3
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4 = y Divide each side by 2. Answer: x = 17, y = 4 Find Missing Values
Example 3
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Find the value of each variable.
A. x = 20, y = 8 B. x = 20, y = 7 C. x = 30, y = 8 D. x = 30, y = 7 Example 3
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Practice and Problem Solving
Pg (15-22) all, (29-32) all DUE by the end of class. What is NOT finished in class becomes homework due the following day.
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